Multivariable equation for a hessian matrix

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I have those two equations and i should find the values to make them equal to 0

3x^2+1-4y=0 -4x-4y=0

I find the values x=-1 and y=1 but the book says there should be also another solution but i cannot find it after doing multiple tries.

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$$3x^2+1-4y=0$$ $$-4x-4y=0$$

$$y=-x$$

$$3x^2+1+4x=0$$

$$(3x+1)(x+1)=0$$

Hopefully you can see the other solution.